/* FILE cokusmt.c */
/* This is a miniscule cleanup of the source downloaded from:  */
/*       http://www.math.keio.ac.jp/~matumoto/ver980409.html   */

/* This is the "Mersenne Twister" random number generator MT19937,
// which generates pseudorandom integers uniformly distributed in
// 0..(2^32 - 1) starting from any odd seed in 0..(2^32 - 1).  This
// version is a recode by Shawn Cokus (Cokus@math.washington.edu) on
// March 8, 1998 of a version by Takuji Nishimura (who had suggestions
// from Topher Cooper and Marc Rieffel in July-August 1997).
//
// Effectiveness of the recoding (on Goedel2.math.washington.edu, a
// DEC Alpha running OSF/1) using GCC -O3 as a compiler: before
// recoding: 51.6 sec. to generate 300 million random numbers; after
// recoding: 24.0 sec. for the same (i.e., 46.5% of original time),
// so speed is now about 12.5 million random number generations per
// second on this machine.
//
// According to URL <http://www.math.keio.ac.jp/~matumoto/emt.html>
// (and paraphrasing a bit in places), the Mersenne Twister is
// "designed with consideration of the flaws of various existing
// generators," has a period of 2^19937 - 1, gives a sequence that
// is 623-dimensionally equidistributed, and "has passed many
// stringent tests, including the die-hard test of G. Marsaglia and
// the load test of P. Hellekalek and S. Wegenkittl."  It is efficient
// in memory usage (typically using 2506 to 5012 bytes of static data,
// depending on data type sizes, and the code is quite short as well).
// It generates random numbers in batches of 624 at a time, so the
// caching and pipelining of modern systems is exploited. It is also
// divide- and mod-free.
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public License
// as published by the Free Software Foundation (either version 2 of
// the License or, at your option, any later version).  This library
// is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY, without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General
// Public License for more details.  You should have received a copy
// of the GNU Library General Public License along with this library;
// if not, write to the Free Software Foundation, Inc., 59 Temple
// Place, Suite 330, Boston, MA 02111-1307, USA.
//
// The code as Shawn received it included the following notice:
//
//  Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura.  When
//  you use this, send an e-mail to <matumoto@math.keio.ac.jp> with
//  an appropriate reference to your work.
//
// It would be nice to CC: <Cokus@math.washington.edu> when you write.
*/

/* uint32 must be an unsigned integer type capable of holding at least
// 32 bits; exactly 32 should be fastest, but 64 is better on an Alpha
// with GCC at -O3 optimization so try your options and see what's
// best for you.
*/

#include "cokusmt.h"

typedef unsigned long uint32;


#define N             (624)               /* length of state vector */
#define M             (397)                 /*   a period parameter */
#define K             (0x9908B0DFU)         /*     a magic constant */
#define hiBit(u)      ((u) & 0x80000000U)   /* mask all but highest */
                                            /*            bit of u  */
#define loBit(u)      ((u) & 0x00000001U)   /* mask all but lowest  */
                                            /*            bit of u  */
#define loBits(u)     ((u) & 0x7FFFFFFFU)   /* mask off the highest */
                                            /*            bit of u  */
#define mixBits(u, v) (hiBit(u) | loBits(v))  /* move hi bit of u   */
                                              /*   to hi bit of v */

static uint32 state[N+1]; /* state vector+1 to not violate ANSI C */
static uint32 *next;      /* next random value computed from here */
static int     left = -1; /* can *next++ this many times before */
                          /* reloading */


/* We initialize state[0..(N-1)] via the generator
//
//   x_new = (69069 * x_old) mod 2^32
//
// from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's
// _The Art of Computer Programming_, Volume 2, 3rd ed.
//
// Notes (SJC): I do not know what the initial state requirements
// of the Mersenne Twister are, but it seems this seeding generator
// could be better.  It achieves the maximum period for its modulus
// (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if
// x_initial can be even, you have sequences like 0, 0, 0, ...;
// 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31,
// 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below.
//
// Even if x_initial is odd, if x_initial is 1 mod 4 then
//
//            low bit of x is always 1,
//    next-to-low bit of x is always 0,
//   2nd-from-low bit of x alternates   ... 0 1 0 1 0 1 0 1 ... ,
//   3rd-from-low bit of x 4-cycles     ... 0 1 1 0 0 1 1 0 ... ,
//   4th-from-low bit of x has 8-cycle  ... 0 0 0 1 1 1 1 0 ... ,
//    ...
//
// and if x_initial is 3 mod 4 then
//
//            low bit of x is always 1,
//    next-to-low bit of x is always 1,
//   2nd-from-low bit of x alternates   ... 0 1 0 1 0 1 0 1 ... ,
//   3rd-from-low bit of x 4-cycles     ... 0 0 1 1 0 0 1 1 ... ,
//   4th-from-low bit of x has 8-cycle  ... 0 0 1 1 1 1 0 0 ... ,
//    ...
//
// The generator's potency (min. s>=0 with (69069-1)^s = 0
// mod 2^32) is 16, which seems to be alright by p. 25, Sec.
// 3.2.1.3 of Knuth.  It also does well in the dimension 2..5
// spectral tests, but it could be better in dimension 6
// (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth).
//
// Note that the random number user does not see the values
// generated here directly since reloadMT() will always munge
// them first, so maybe none of all of this matters.  In fact,
// the seed values made here could even be extra-special
// desirable if the Mersenne Twister theory says so-- that's
// why the only change I made is to restrict to odd seeds.
*/
void seedMT(uint32 seed)
{
   register uint32  x = (seed | 1U) & 0xFFFFFFFFU,
                   *s = state;
   register int     j;

   for (left = 0, *s++ = x, j = N;
        --j;
        *s++ = (x *= 69069U) & 0xFFFFFFFFU);
} /* seedMT */


static uint32 reloadMT(void)
{
   register  uint32
            *p0    = state,
            *p2    = state + 2,
            *pM    = state + M,
            s0,
            s1;
   register int    j;

   if (left < -1)  seedMT(4357U);        /* Autoseed on first use */

   left = N - 1; next = state + 1;
   for (s0 = state[0], s1 = state[1], j = N - M + 1;
             --j;
             s0 = s1, s1 = *p2++)
      *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);

   for (pM = state, j = M;
             --j;
             s0 = s1, s1 = *p2++)
      *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);

   s1 = state[0];
   *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U);
   s1 ^= (s1 >> 11);
   s1 ^= (s1 <<  7) & 0x9D2C5680U;
   s1 ^= (s1 << 15) & 0xEFC60000U;
   return (s1 ^ (s1 >> 18));
} /* reloadMT */


uint32 randomMT(void)
{
   uint32 y;

   if (--left < 0)
      return(reloadMT());

   y  = *next++;
   y ^= (y >> 11);
   y ^= (y <<  7) & 0x9D2C5680U;
   y ^= (y << 15) & 0xEFC60000U;
   return (y ^ (y >> 18));
} /* randomMT */

